My dad passed away and all of his paper that was in a plastic file container is now missing. We believe by mistake they were thrown away. He has no will or execitor.
He had told his grandson he could have his car when he passed but now with out the title we cant. He did sign the gift form in the beginning of 2013 due to his illness.What are my options?

First step is someone needs to petition the probate court to be named executor. The logical choice is any of his children (you?) or other close relatives, but it really needs to be someone who can put in the time necessary and whom the other interested parties can feel is trustworthy. The executor's job is to settle your father's remaining bills (I assume you have already taken care of funeral arrangements?), and then make sure that remaining assets in his estate are partitioned to the heirs in accordance with state law given that he has no will. In general that means if he has no widow his assets get divided up evenly among his children per stirpes, but intestate laws vary by state so it really depends on what state he lived in. Once an executor is named that person can then approach the DMV about getting a replacement title in the name of the heir for the car. You can call the DMV to find out what the process is to do that - typically the executior will need a copy of the death certificate plus "letters testimentary" documenting he is indeed the lawful executor. But the process varies tremendously from state to state, so the executoe should contact the DMV and see what they need.

One issue here is that while your father may have verbally said the car goes to his grandchild, without a will the law says it goes to his children instead. The executor must follow the law. However, if the executor talks this over with all the lawful heirs and if no one objects the executor could just make it so, but if any of the legal heirs object then the car cannot go to the grandchild. One way around this: the car could go to one of the children and then that person could gift it to the grandchild.

Please clarify what you meant by "he did sign the gift form" - what gift form?

In my state there is a DMV gift form for close relatives to get out of paying sales tax.
But now that the dad is deceased, I don't think that form is any good.
I went through this when my dad died (I was taking care of him and had his car anyway) and to go through the court and deal with really complicated DMV rules, including going far away from my closest DMV office, would have been awful. So I pretended he was still alive. I made an educated guess that the DMV doesn't cross check with death records. In fact I drove it in his name for 11 months because we had just paid his insurance on the car a month before he died.

I'm not suggesting that OP apply for a lost title replacement in the dad's name at all, because that is even more complicated. He has to find out from his DMV what the process is for this. It varies by state.

In many states there is an abbreviated procedure, whereby many of the complications of probate (court proceeding regarding decedents' estates) can be avoided. It varies from state to state, but generally entails signing an affidavit to the effect that the decedent's estate is under a certain amount, doesn't include real property, or whatever. You might check into that for whichever state you are in.

Also, if the car is given by the (intestate) heirs-at-law to the grandson, I suspect the gift form would work.